/* * Copyright (c) 2018-2021, Andreas Kling * All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions are met: * * 1. Redistributions of source code must retain the above copyright notice, this * list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright notice, * this list of conditions and the following disclaimer in the documentation * and/or other materials provided with the distribution. * * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, * OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ #include #include #include TEST_CASE(trig) { EXPECT_APPROXIMATE(sin(1234), 0.601927); EXPECT_APPROXIMATE(cos(1234), -0.798550); EXPECT_APPROXIMATE(tan(1234), -0.753775); EXPECT_APPROXIMATE(sqrt(1234), 35.128336); EXPECT_APPROXIMATE(sin(-1), -0.8414709848078965); EXPECT_APPROXIMATE(cos(-1), 0.5403023058681398); EXPECT_APPROXIMATE(tan(-1), -1.5574077246549023); EXPECT(isnan(sqrt(-1))); EXPECT(isnan(asin(1.1))); EXPECT(isnan(asin(-1.1))); EXPECT_APPROXIMATE(asin(0), 0.0); EXPECT_APPROXIMATE(asin(0.01), 0.01); EXPECT_APPROXIMATE(asin(0.1), 0.100167); EXPECT_APPROXIMATE(asin(0.3), 0.304693); EXPECT_APPROXIMATE(asin(0.499), 0.522444); EXPECT_APPROXIMATE(asin(0.5), 0.523599); EXPECT_APPROXIMATE(asin(0.501), 0.524754); EXPECT_APPROXIMATE(asin(0.9), 1.119770); EXPECT_APPROXIMATE(asin(0.99), 1.429245); EXPECT_APPROXIMATE(asin(1.0), 1.570750); EXPECT_APPROXIMATE(atan(0), 0.0); EXPECT_APPROXIMATE(atan(0.5), 0.463648); EXPECT_APPROXIMATE(atan(-0.5), -0.463648); EXPECT_APPROXIMATE(atan(5.5), 1.390943); EXPECT_APPROXIMATE(atan(-5.5), -1.390943); EXPECT_APPROXIMATE(atan(555.5), 1.568996); } TEST_CASE(other) { EXPECT_EQ(trunc(9999999999999.5), 9999999999999.0); EXPECT_EQ(trunc(-9999999999999.5), -9999999999999.0); } TEST_CASE(exponents) { struct values { double x; double exp; double sinh; double cosh; double tanh; }; values values[8] { { 1.500000, 4.481626, 2.129246, 2.352379, 0.905148 }, { 20.990000, 1304956710.432035, 652478355.216017, 652478355.216017, 1.000000 }, { 20.010000, 490041186.687082, 245020593.343541, 245020593.343541, 1.000000 }, { 0.000000, 1.000000, 0.000000, 1.000000, 0.000000 }, { 0.010000, 1.010050, 0.010000, 1.000050, 0.010000 }, { -0.010000, 0.990050, -0.010000, 1.000050, -0.010000 }, { -1.000000, 0.367879, -1.175201, 1.543081, -0.761594 }, { -17.000000, 0.000000, -12077476.376788, 12077476.376788, -1.000000 }, }; for (auto& v : values) { EXPECT_APPROXIMATE(exp(v.x), v.exp); EXPECT_APPROXIMATE(sinh(v.x), v.sinh); EXPECT_APPROXIMATE(cosh(v.x), v.cosh); EXPECT_APPROXIMATE(tanh(v.x), v.tanh); } EXPECT_EQ(exp(1000), __builtin_huge_val()); } TEST_CASE(logarithms) { EXPECT(isnan(log(-1))); EXPECT(log(0) < -1000000); EXPECT_APPROXIMATE(log(0.5), -0.693233); EXPECT_APPROXIMATE(log(1.1), 0.095310); EXPECT_APPROXIMATE(log(5), 1.609480); EXPECT_APPROXIMATE(log(5.5), 1.704842); EXPECT_APPROXIMATE(log(500), 6.214104); EXPECT_APPROXIMATE(log2(5), 2.321989); EXPECT_APPROXIMATE(log10(5), 0.698988); } union Extractor { explicit Extractor(double d) : d(d) { } Extractor(unsigned sign, unsigned exponent, unsigned long long mantissa) : mantissa(mantissa) , exponent(exponent) , sign(sign) { } struct { unsigned long long mantissa : 52; unsigned exponent : 11; unsigned sign : 1; }; double d; bool operator==(const Extractor& other) const { return other.sign == sign && other.exponent == exponent && other.mantissa == mantissa; } }; namespace AK { template<> struct Formatter : StandardFormatter { void format(FormatBuilder& builder, const Extractor& value) { builder.put_literal("{"); builder.put_u64(value.sign); builder.put_literal(", "); builder.put_u64(value.exponent, 16, true); builder.put_literal(", "); builder.put_u64(value.mantissa, 16, true); builder.put_literal("}"); } }; } static Extractor nextafter_translator(Extractor x, Extractor target) { return Extractor(nextafter(x.d, target.d)); } TEST_CASE(nextafter) { EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x7fe, 0xfffffffffffff), Extractor(0x0, 0x7fe, 0xfffffffffffff)), Extractor(0x0, 0x7fe, 0xfffffffffffff)); EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x1, 0x0), Extractor(0x0, 0x412, 0xe848000000000)), Extractor(0x0, 0x1, 0x1)); EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x3ff, 0x0), Extractor(0x0, 0x412, 0xe848200000000)), Extractor(0x0, 0x3ff, 0x1)); EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x0, 0x0), Extractor(0x0, 0x412, 0xe848000000000)), Extractor(0x0, 0x0, 0x1)); EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x0), Extractor(0x0, 0x412, 0xe848000000000)), Extractor(0x0, 0x0, 0x1)); EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x3ff, 0x0), Extractor(0x0, 0x412, 0xe847e00000000)), Extractor(0x1, 0x3fe, 0xfffffffffffff)); EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x1), Extractor(0x0, 0x412, 0xe848000000000)), Extractor(0x0, 0x0, 0x2)); EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x7fe, 0xfffffffffffff), Extractor(0x0, 0x7fe, 0xfffffffffffff)), Extractor(0x0, 0x7fe, 0xfffffffffffff)); EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x412, 0xe848000000000), Extractor(0x0, 0x1, 0x0)), Extractor(0x0, 0x412, 0xe847fffffffff)); EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x412, 0xe848200000000), Extractor(0x0, 0x3ff, 0x0)), Extractor(0x0, 0x412, 0xe8481ffffffff)); EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x412, 0xe848000000000), Extractor(0x1, 0x0, 0x0)), Extractor(0x0, 0x412, 0xe847fffffffff)); EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x412, 0xe848000000000), Extractor(0x0, 0x0, 0x0)), Extractor(0x0, 0x412, 0xe847fffffffff)); EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x412, 0xe847e00000000), Extractor(0x1, 0x3ff, 0x0)), Extractor(0x0, 0x412, 0xe847dffffffff)); EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x412, 0xe848000000000), Extractor(0x0, 0x0, 0x1)), Extractor(0x0, 0x412, 0xe847fffffffff)); EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x7fe, 0xfffffffffffff), Extractor(0x0, 0x7fe, 0xfffffffffffff)), Extractor(0x0, 0x7fe, 0xfffffffffffff)); EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x1, 0x0), Extractor(0x0, 0x1, 0x0)), Extractor(0x0, 0x1, 0x0)); EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x3ff, 0x0), Extractor(0x0, 0x3ff, 0x0)), Extractor(0x0, 0x3ff, 0x0)); EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x0, 0x0), Extractor(0x1, 0x0, 0x0)), Extractor(0x1, 0x0, 0x0)); EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x0), Extractor(0x0, 0x0, 0x0)), Extractor(0x0, 0x0, 0x0)); EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x3ff, 0x0), Extractor(0x1, 0x3ff, 0x0)), Extractor(0x1, 0x3ff, 0x0)); EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x1), Extractor(0x0, 0x0, 0x1)), Extractor(0x0, 0x0, 0x1)); EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x7fe, 0xfffffffffffff), Extractor(0x0, 0x7fe, 0xfffffffffffff)), Extractor(0x1, 0x7fe, 0xffffffffffffe)); EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x1, 0x0), Extractor(0x0, 0x1, 0x0)), Extractor(0x1, 0x0, 0xfffffffffffff)); EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x3ff, 0x0), Extractor(0x0, 0x3ff, 0x0)), Extractor(0x1, 0x3fe, 0xfffffffffffff)); EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x0), Extractor(0x1, 0x0, 0x0)), Extractor(0x1, 0x0, 0x0)); EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x0, 0x0), Extractor(0x0, 0x0, 0x0)), Extractor(0x0, 0x0, 0x0)); EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x3ff, 0x0), Extractor(0x1, 0x3ff, 0x0)), Extractor(0x0, 0x3fe, 0xfffffffffffff)); EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x0, 0x1), Extractor(0x0, 0x0, 0x1)), Extractor(0x1, 0x0, 0x0)); EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x7fe, 0xfffffffffffff), Extractor(0x1, 0x7fe, 0xfffffffffffff)), Extractor(0x0, 0x7fe, 0xffffffffffffe)); EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x1, 0x0), Extractor(0x1, 0x1, 0x0)), Extractor(0x0, 0x0, 0xfffffffffffff)); EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x3ff, 0x0), Extractor(0x1, 0x3ff, 0x0)), Extractor(0x0, 0x3fe, 0xfffffffffffff)); EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x0, 0x0), Extractor(0x0, 0x0, 0x0)), Extractor(0x0, 0x0, 0x0)); EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x0), Extractor(0x1, 0x0, 0x0)), Extractor(0x1, 0x0, 0x0)); EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x3ff, 0x0), Extractor(0x0, 0x3ff, 0x0)), Extractor(0x1, 0x3fe, 0xfffffffffffff)); EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x1), Extractor(0x1, 0x0, 0x1)), Extractor(0x0, 0x0, 0x0)); EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x7fe, 0xfffffffffffff), Extractor(0x0, 0x7fe, 0xfffffffffffff)), Extractor(0x0, 0x7fe, 0xfffffffffffff)); EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x1, 0x0), Extractor(0x1, 0x419, 0x7d78400000000)), Extractor(0x0, 0x0, 0xfffffffffffff)); EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x3ff, 0x0), Extractor(0x1, 0x419, 0x7d783fc000000)), Extractor(0x0, 0x3fe, 0xfffffffffffff)); EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x0, 0x0), Extractor(0x1, 0x419, 0x7d78400000000)), Extractor(0x1, 0x0, 0x1)); EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x0), Extractor(0x1, 0x419, 0x7d78400000000)), Extractor(0x1, 0x0, 0x1)); EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x3ff, 0x0), Extractor(0x1, 0x419, 0x7d78404000000)), Extractor(0x1, 0x3ff, 0x1)); EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x1), Extractor(0x1, 0x419, 0x7d78400000000)), Extractor(0x0, 0x0, 0x0)); EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x7fe, 0xfffffffffffff), Extractor(0x0, 0x7fe, 0xfffffffffffff)), Extractor(0x0, 0x7fe, 0xfffffffffffff)); EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x419, 0x7d78400000000), Extractor(0x0, 0x1, 0x0)), Extractor(0x1, 0x419, 0x7d783ffffffff)); EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x419, 0x7d783fc000000), Extractor(0x0, 0x3ff, 0x0)), Extractor(0x1, 0x419, 0x7d783fbffffff)); EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x419, 0x7d78400000000), Extractor(0x1, 0x0, 0x0)), Extractor(0x1, 0x419, 0x7d783ffffffff)); EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x419, 0x7d78400000000), Extractor(0x0, 0x0, 0x0)), Extractor(0x1, 0x419, 0x7d783ffffffff)); EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x419, 0x7d78404000000), Extractor(0x1, 0x3ff, 0x0)), Extractor(0x1, 0x419, 0x7d78403ffffff)); EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x419, 0x7d78400000000), Extractor(0x0, 0x0, 0x1)), Extractor(0x1, 0x419, 0x7d783ffffffff)); } TEST_CASE(scalbn) { EXPECT(isnan(scalbn(NAN, 3))); EXPECT(!isfinite(scalbn(INFINITY, 5))); EXPECT_EQ(scalbn(0, 3), 0); EXPECT_EQ(scalbn(15.3, 0), 15.3); EXPECT_EQ(scalbn(0x0.0000000000008p-1022, 16), 0x0.0000000000008p-1006); static constexpr auto biggest_subnormal = DBL_MIN - DBL_TRUE_MIN; auto smallest_normal = scalbn(biggest_subnormal, 1); Extractor ex(smallest_normal); EXPECT(ex.exponent != 0); EXPECT_EQ(scalbn(2.0, 4), 32.0); } TEST_MAIN(Math)